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Probability and Computational Finance Seminar
Xiang Yu
Title: Utility Maximization with Addictive Consumption Habits in Incomplete Market

Abstract: We study the problem of utility maximization of consumption together with addictive habit formation in a general incomplete semimartingale financial market. By introducing the properly defined auxiliary state process and modified dual space as well as treating the multi-variables of value function as both initial wealth and initial habit, we embed our original path dependent problem into an abstract auxiliary time separable utility maximization problem with some shadow random endowment. We establish existence and uniqueness of the optimal solution using convex duality approach on the product space. We also provide market independent sufficient conditions on both the unbounded optional discounting factors and the utility functions (i.e., reasonable asymptotic elasticity conditions on both U and V) for the validity of several key assertions of our main results to hold true.

Pdf File: Xiang_Yu.pdf
Date: Monday, September 26, 2011
Time: 5:00 pm
Location: Wean Hall 6423
Submitted by:  Kasper Larsen